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題名: | 半純函數的唯一性 Some Results on the Uniqueness of Meromorphic Functions |
作者: | 陳耿彥 Chen, Keng-Yan |
貢獻者: | 陳天進 Chen, Ten-Ging 陳耿彥 Chen, Keng-Yan |
關鍵詞: | 值分佈理論 半純函數 value distribution theory meromorphic function |
日期: | 2007 | 上傳時間: | 17-九月-2009 | 摘要: | 在這篇論文裡,我們利用值分佈的理論來探討半純函數的共值與唯一性的問題,本文包含了以下的結果:將Jank與Terglane有關三個A類中的半純函數唯一性的結果推廣到任意q個半純函數的情形;證明了C. C. Yang的一個猜測;建構了一類半純函數恰有兩個虧值,而且算出它們的虧格;將\nNevanlinna 五個值的定理推廣至兩個半純函數部分共值的情形;探討純函數\n與其導數的共值問題;最後,證明了兩個半純函數共四個值且重數皆不同的定\n理。 In this thesis, we study the sharing value problems and the\nuniqueness problems of meromorphic functions in the theory of value distribution. In fact, this thesis contains the following results: We generalize a unicity condition of three meromorphic functions given by Jank and Terglane in class A to the case of arbitrary q meromorphic functoins. An elementary proof of a conjecture of C. C. Yang is provided. We construct a class of meromorphic functions with exact two deficient values and their deficiencies are explicitly computed. We generalize the Nevanlinna`s five-value theorem to the cases that two meromorphic functions partially share either five or more values, or five or\nmore small functions. In each case, we formulate a way to measure how far these two meromorphic functions are from sharing either values or small functions, and use this measurement to prove a uniqueness theorem. Also, we prove some uniqueness theorems on entire functions that share a pair of values (a,-a) with their derivatives, which are reformulations of some important results about uniqueness of entire functions that share values with their derivatives. Finally, we prove that if two distinct non-constant meromorphic functions $f$ and $g$ share four distinct values a_1, a_2, a_3, a_4 DM such that each a_i-point is either a (p,q)-fold or (q,p)-fold point of f and g, then (p,q) is either (1,2) or (1,3) and f, g are in some particular forms. |
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描述: | 博士 國立政治大學 應用數學研究所 93751501 96 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0093751501 | 資料類型: | thesis |
Appears in Collections: | 學位論文 |
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